This work is devoted to the investigation of evolution of intense quasi-monochromatic signals in the case of infinite acoustic Reynolds numbers. The consideration is based on the zero viscocity limit solution of the Burgers equation, which reduces the Hopf-Cole solution to a "maximum" principle. This limit solution permits an easy way to get the profile of the waves, position of shocks and their velocities at arbitrary times. The process of transformation of an initial quasi-monochromatic wave into a sawtooth wave is considered. It is shown that the nonlinearity leads to suppression of the initial amplitude modulation and to the transformation of the initial frequency modulation into a shock amplitude modulation. The amplitude of the low frequency component generated by a quasi-monochromatic wave is found. It is shown that the interaction of this component with high frequency waves leads to phase modulation, which increases with distance. The amplitudes of the new components of the spectrum are found. It is shown that when the value of phase modulation is small, the amplitudes of the satellites do not depend on the distance or the number of harmonics of the primary wave.

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Document Type: Research Article

Publication date: 1998-05-01

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Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.